# BC vs. Calculus AB

## What's the Difference?

BC (Calculus BC) and Calculus AB are both advanced placement courses in calculus offered in high schools. Calculus AB is an introductory course that covers the basic concepts of calculus, including limits, derivatives, and integrals. It provides students with a solid foundation in calculus and prepares them for further studies in mathematics and science. On the other hand, BC is an extension of AB and covers additional topics such as infinite series, parametric equations, and polar coordinates. BC is more rigorous and comprehensive, allowing students to delve deeper into the subject and gain a more advanced understanding of calculus. Overall, while both courses cover calculus, BC offers a more extensive and in-depth curriculum.

## Comparison

Attribute | BC | Calculus AB |
---|---|---|

Course Length | Full year | Full year |

Topics Covered | Includes all topics covered in Calculus AB, plus additional topics such as series, parametric equations, and polar coordinates. | Covers limits, derivatives, integrals, and applications of these concepts. |

Exam Format | Multiple-choice and free-response questions | Multiple-choice and free-response questions |

College Credit | May earn college credit for Calculus I and Calculus II | May earn college credit for Calculus I |

Prerequisites | Successful completion of precalculus or equivalent | Successful completion of precalculus or equivalent |

Advanced Placement (AP) Exam | BC Exam | AB Exam |

Topics Covered in AB Portion | N/A | Limits, derivatives, integrals, and applications of these concepts |

Topics Covered in BC Portion | Series, parametric equations, polar coordinates, and additional topics | N/A |

## Further Detail

### Introduction

Calculus is a fundamental branch of mathematics that deals with the study of change and motion. It is divided into two main courses in high school: Calculus AB and Calculus BC. While both courses cover similar topics, there are distinct differences in the depth and breadth of the material covered. In this article, we will explore the attributes of BC and Calculus AB, highlighting their similarities and differences.

### Course Content

Calculus AB is typically considered an introductory course to calculus. It covers the basic concepts of limits, derivatives, and integrals. Students in Calculus AB learn how to find derivatives of functions, solve optimization problems, and calculate definite and indefinite integrals. The course provides a solid foundation in calculus and prepares students for further studies in mathematics, science, or engineering.

On the other hand, Calculus BC is an extension of Calculus AB. It covers all the topics taught in Calculus AB but goes into greater depth and introduces additional concepts. In Calculus BC, students delve deeper into integration techniques, including integration by parts, partial fractions, and trigonometric substitution. They also learn about sequences and series, including convergence and divergence tests. Calculus BC provides a more comprehensive understanding of calculus and is often taken by students who are particularly interested in mathematics or pursuing a STEM-related field.

### Exam Structure

The Advanced Placement (AP) Calculus AB and BC exams are designed to assess students' understanding of calculus concepts and their ability to apply them. Both exams consist of two sections: multiple-choice and free-response.

The multiple-choice section in both exams includes questions that test students' knowledge of calculus concepts, problem-solving skills, and their ability to interpret and analyze functions and graphs. This section is worth 50% of the total exam score.

The free-response section in Calculus AB consists of six questions, while Calculus BC has nine questions. These questions require students to show their work and provide detailed explanations. The free-response section assesses students' ability to solve problems, apply calculus concepts to real-world scenarios, and communicate their mathematical reasoning effectively. It is worth 50% of the total exam score.

While the structure of the exams is similar, Calculus BC covers additional topics, so the free-response section in BC may include questions on those advanced concepts. This means that students taking Calculus BC have a broader range of topics to prepare for in the free-response section compared to those taking Calculus AB.

### College Credit and Placement

Both Calculus AB and BC are Advanced Placement courses, meaning that students have the opportunity to earn college credit or advanced placement in college if they perform well on the AP exam. However, the amount of credit and placement opportunities may vary depending on the college or university.

Typically, a score of 3 or higher on the AP Calculus AB exam can earn students credit for a semester of calculus in college. Some colleges may also grant advanced placement, allowing students to skip introductory calculus courses and move directly into more advanced math courses.

On the other hand, a score of 3 or higher on the AP Calculus BC exam often grants students credit for two semesters of calculus in college. Additionally, students who perform well on the BC exam may be eligible for advanced placement, allowing them to start their college math journey at a higher level.

It is important for students to research the credit and placement policies of the colleges they are interested in to understand how their AP Calculus exam scores will be recognized.

### Preparation and Prerequisites

Both Calculus AB and BC require a strong foundation in algebra, geometry, and precalculus. It is recommended that students take a precalculus course before enrolling in either Calculus AB or BC to ensure they have the necessary mathematical background.

For students considering Calculus BC, it is particularly important to have a solid understanding of the topics covered in Calculus AB. Since BC builds upon the concepts taught in AB, students who have not taken Calculus AB may find it challenging to keep up with the pace and depth of the BC course.

When it comes to exam preparation, students in both Calculus AB and BC should practice solving a variety of calculus problems, review key concepts, and familiarize themselves with the format of the AP exam. There are numerous study resources available, including textbooks, online courses, and practice exams, to help students prepare effectively.

### Conclusion

Calculus AB and BC are both valuable courses that provide students with a strong foundation in calculus. Calculus AB serves as an introductory course, covering the fundamental concepts of limits, derivatives, and integrals. On the other hand, Calculus BC extends the material covered in AB, delving deeper into integration techniques and introducing topics like sequences and series.

While both courses have similar exam structures, Calculus BC covers additional topics, making the free-response section more comprehensive. The amount of college credit and placement opportunities also varies between AB and BC, with BC often offering more credit and advanced placement options.

Ultimately, the choice between Calculus AB and BC depends on the student's interest in mathematics, their future academic goals, and the level of depth they wish to explore in calculus. Regardless of the course chosen, both Calculus AB and BC provide a solid foundation for further studies in mathematics, science, and engineering.

Comparisons may contain inaccurate information about people, places, or facts. Please report any issues.